THE MATHEMATICAL MODELLING IN THE COMPUTER TOMOGRAPHY WITH USING DIRECT FOURIER METHOD AND SPLINE - INTERLINEATION OF THE FUNCTIONS

摘要

The article is devoted to improvement of mathematical model a X-ray computer tomograph on the basis of direct method Fourier, kvadrature formulas with even number of knots, exact on polynomials and splines of the second order and a spline - interlineation of functions of two variables. This kvadrature formula removes restrictions on parity or oddness of number of projections, acting on PC from a computer tomograph. It can be used (together with kvadrature Simpson's formula, demanding the odd number of knots) in serial tomographs. On a basis a spline - interlineation of functions with property f(x, y) = f(y, x) are development such updating of direct Fourier method which allows to reduce asymptotical twice quantity of arithmetic operations. The algorithm on basis FFT for effective calculation of full Fourier sums of two variables is developed. The algorithm is used at visualization in mathematical model X-ray tomographs.